The relationship of neural computation and inference has long been investigated (see, e.g., McCulloch, W. S. and Pitts, “A Logical Calculus of Ideas Immanent in Neuron Activity,” Bulletin of Mathematical Biology 5, pp. 115-133 (1943); Baum, E. B. and Wilczek, F., “Supervised Learning of Probability Distributions by Neural Networks,” Neural Information Processing Systems, pp. 52-61 (1988); and Hopfield, J. J., “Learning Algorithm and Probability Distributions in Feed-Forward and Feed-Back Networks,” Proceeding of the National Academy of Science, pp. 8429-8433 (1987)). Most of these researchers use neural network computation to explain the origin of Boolean logic or the connection with probability inference. When dealing with the logical truth of a proposition or the belief of a hypothesis, there are many terms associated with it, including certainty factor, support, confirmation and confidence level.
Historically these are considered subjective or epistemic, which is not the same as chance or aleatory probability that is associated with a random variable. Although conceptually different, whether the epistemic probability should follow the same rule as aleatory probability has always been at the center of debate. If the epistemic probability has a different rule, then it must come from the law of thought, or more precisely, the emergent property of neural computation.
Neural processing is often aimed at detecting differences in action potential rather than absolute values. For example, neural processing detects contrast rather than pure luminance, edges rather than areas, and so on. In evidential reasoning the difference in action potential means the weight of evidence favors the hypothesis, which in turn can be transformed into the belief of the possibility measure. The competitive nature of neuron activities induces the belief judgment.
A plausible neural network (PLANN) model that can compute probabilistic and possibilistic and other kinds of fuzzy logic is described herein. The learning algorithm of PLANN is discussed in U.S. patent application Ser. No. 09/808,101, which is incorporated herein by reference in its entirety. The present application describes a more detailed architecture and activation model of PLANN, which facilitates the computation of PLANN inference.